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The Grid-Pyramid: A Generalized Pyramid Network

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Abstract

The Pyramid network is a desirable network topology used as both software data-structure and hardware architecture. In this paper, we propose a general definition for a class of pyramid networks that are based on grid connections between the nodes in each level. Contrary to the conventional pyramid network in which the nodes in each level form a mesh, the connections between these nodes may also be according to other grid-based topologies such as the torus, hypermesh or WK-recursive. Such pyramid networks form a wide class of interconnection networks that possess rich topological properties. We study a number of important properties of these topologies for general-purpose parallel processing applications. In particular, we prove that such pyramids are Hamiltonian-connected, i.e. for any arbitrary pair of nodes in the network there exists at least one Hamiltonian path between the two given nodes, and pancyclic, i.e. any cycle of length 3, 4 … and N, can be embedded in a given N-node pyramid network. It is also proven that two link-disjoint Hamiltonian cycles exist in the torus-pyramid and hypermesh-pyramid networks.

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Authors and Affiliations

  1. IPM School of Computer Science, Tehran, Iran

    M. R. HoseinyFarahabady & H. Sarbazi-Azad

  2. Sharif University of Technology, Tehran, Iran

    H. Sarbazi-Azad

Authors
  1. M. R. HoseinyFarahabady
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  2. H. Sarbazi-Azad
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Correspondence to H. Sarbazi-Azad.

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HoseinyFarahabady, M.R., Sarbazi-Azad, H. The Grid-Pyramid: A Generalized Pyramid Network. J Supercomput 37, 23–45 (2006). https://doi.org/10.1007/s11227-006-4598-4

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  • DOI: https://doi.org/10.1007/s11227-006-4598-4

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